Suppose we have written $$\sup_n f_n$$ and $$\lim_{n\to\infty}\sup_n f_n$$
How am I to understand the difference between the two?
2026-03-25 16:45:41.1774457141
Supremum vs limit supremum; notation confusion
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To avoid confusion, it is best to write $$ \limsup_{n\to\infty} f_n \tag{1}$$ and never write $$ \lim_{n\to\infty}\sup_n f_n \tag{2}$$ since (2) is just wrong. Your textbook should have a definition for (1).